Fuzzy dominance rules for real-world many objective optimization

In real world optimization problems there are often multiple objectives to consider. However, with traditional multi-objective optimization algorithms, like the Non-Dominated Sorting Genetic Algorithm, NSGA-II, one solution is not produced at the end of the process but a set of non-dominated solutions. This set of solutions make up what is known as the Pareto front. The Pareto front relies on calculating the dominance of each solution the multi-objective algorithm produces. Traditional dominance calculations are reasonable for a small number of objectives. However, the more objectives there are in the problem, the more unsuitable these dominance calculations become. This leads to poor selection criteria and ultimately a weaker form of optimization when compared to a small number of objectives. In this paper, we present a fuzzy logic system for computing dominance between two solutions. We have evaluated this fuzzy logic system in optimizing a set of black box test problems. In addition, we have also applied it to a real world many-objective system that optimizes five conflicting objectives, in the telecommunications domain. The implementation of the fuzzy logic system has led to the NSGA-II algorithm with Fuzzy Dominance Rules (FDRs) being able to perform better in a number of black box tests and improving the results of our real-world many-objective optimization problem, with a statistically significant improvement to the hypervolume of 5.46%.